{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hamiltonian Neural Networks\n",
    "\n",
    "In this tutorial we train **Hamiltonian Neural Networks** (HNNs), a useful tool to learn simmetries and conservation laws from data, firstly introduced in [Greydanus S., et al., 2019](https://arxiv.org/abs/1906.01563).\n",
    "\n",
    "Let $q\\in\\mathbb{R}^n$ be a vector of generalized positions and let $p\\in\\mathbb{R}^n$ be the corresponding generalized momenta. Roughly speaking, HNNs mimick the canonical equations of classical mechanics\n",
    "\n",
    "$$\n",
    "    \\begin{aligned}\n",
    "        &\\dot q = \\nabla_p\\mathcal{H}(q,p)\\\\\n",
    "        &\\dot p = -\\nabla_q\\mathcal{H}(q,p)\n",
    "    \\end{aligned}\n",
    "$$\n",
    "\n",
    "where the Hamiltonian function $\\mathcal{H}$ is parametrized by a neural network $\\mathcal H_\\theta(q, p)$. In the original paper, provided a dataset of tuples $(\\dot q, \\dot p)$ generated by some conservative dynamical process, the HNN is trained (the parameters of $\\mathcal{H}$ optimized) to minimize a loss of type\n",
    "\n",
    "$$\n",
    "    \\ell_\\theta := || \\dot q - \\nabla_p\\mathcal H_\\theta||_2^2 + || \\dot p + \\nabla_q\\mathcal H_\\theta||_2^2 \n",
    "$$\n",
    "\n",
    "We hereby show how to implement this experiment in torchdyn for a simple mass-spring system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../')\n",
    "from torchdyn.models import *\n",
    "from torchdyn import *\n",
    "from torchdyn.datasets import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vector field of an HNN, to be passed to our `DEFunc` can be simply defined as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "class HNN(nn.Module):\n",
    "    def __init__(self, Hamiltonian:nn.Module, dim=1):\n",
    "        super().__init__()\n",
    "        self.H = Hamiltonian\n",
    "        self.n = dim\n",
    "    def forward(self, x):\n",
    "        with torch.set_grad_enabled(True):\n",
    "            x = x.requires_grad_(True)\n",
    "            gradH = torch.autograd.grad(self.H(x).sum(), x, allow_unused=False, create_graph=True)[0] \n",
    "        return torch.cat([gradH[:,self.n:], -gradH[:,:self.n]], 1).to(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider a 1D mass-spring system\n",
    "\n",
    "$$\n",
    "    m\\ddot x - kx = 0,~~x(0)=0,~~\\dot x(0)=1\n",
    "$$\n",
    "\n",
    "and we let $q=x$, $p=\\dot x$. We then train the neural network on data generated from a single trajectory of the system\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"Static\" Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "t = torch.linspace(0,1, 100).reshape(-1,1)\n",
    "X = torch.cat([\n",
    "    torch.sin(2*np.pi*t),\n",
    "    torch.cos(2*np.pi*t)\n",
    "],1).to(device)\n",
    "\n",
    "y = torch.cat([\n",
    "    torch.cos(2*np.pi*t),\n",
    "    -torch.sin(2*np.pi*t)\n",
    "],1).to(device)\n",
    "\n",
    "train = data.TensorDataset(X, y)\n",
    "trainloader = data.DataLoader(train, batch_size=len(X), shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "        self.c = 0\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model.defunc(0,x)\n",
    "    \n",
    "    def loss(self, y, y_hat):\n",
    "        return ((y-y_hat)**2).sum()\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch      \n",
    "        y_hat = self.model.defunc(0,x)   \n",
    "        loss = self.loss(y_hat, y)\n",
    "        logs = {'train_loss': loss}\n",
    "        return {'loss': loss, 'log': logs}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "HamFunc = HNN(nn.Sequential(\n",
    "            nn.Linear(2,64),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(64,1))).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 257   \n",
      "/home/jyp/michael_dev/testenv/lib/python3.7/site-packages/pytorch_lightning/utilities/distributed.py:25: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 20 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5b33d8f8888e41ac92c5e8386685de9d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = NeuralDE(HamFunc).to(device)\n",
    "\n",
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=500, max_epochs=1000)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, \"HHN's trajectories & training data\")"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sample random initial conditions\n",
    "X_t = torch.randn(1000, 2).to(device)\n",
    "# Evaluate the HNN trajectories for 1s\n",
    "s_span = torch.linspace(0, 1, 100)\n",
    "traj = model.trajectory(X_t, s_span).detach().cpu()\n",
    "\n",
    "# Plot the HHN's trajectories with random ICs\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "color = ['orange', 'blue']\n",
    "for i in range(len(X_t)):\n",
    "    ax.plot(traj[:,i,0], traj[:,i,1], color='blue', alpha=0.1);\n",
    "ax.plot(X[:,0].cpu(),X[:,1].cpu(), color='red')\n",
    "ax.set_xlim([-2,2])\n",
    "ax.set_ylim([-2,2])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"HHN's trajectories & training data\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Learned Hamiltonian & Vector Field')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_grid =  50\n",
    "x = torch.linspace(-3,3,n_grid)\n",
    "Q, P = torch.meshgrid(x,x)\n",
    "H, U, V = torch.zeros(Q.shape), torch.zeros(Q.shape), torch.zeros(Q.shape)\n",
    "for i in range(n_grid):\n",
    "    for j in range(n_grid):\n",
    "        x = torch.cat([Q[i,j].reshape(1,1),P[i,j].reshape(1,1)],1).to(device)\n",
    "        H[i,j] = model.defunc.m.H(x).detach().cpu()\n",
    "        O = model.defunc(0,x).detach().cpu()\n",
    "        U[i,j], V[i,j] = O[0,0], O[0,1]\n",
    "        \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.contourf(Q,P,H,100,cmap='RdYlBu')\n",
    "ax.streamplot(Q.T.numpy(),P.T.numpy(),U.T.numpy(),V.T.numpy(), color='black')\n",
    "ax.set_xlim([Q.min(),Q.max()])\n",
    "ax.set_ylim([P.min(),P.max()])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"Learned Hamiltonian & Vector Field\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## HNNs as General-Purpose Modules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to try using using an HNN as a general-purpose DL module, e.g. for a classification task, you can do it well in `torchdyn`. Let us introduce a simple toy example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate data with torchdyn utilities\n",
    "d = ToyDataset()\n",
    "X, yn = d.generate(n_samples=520, dataset_type='moons', noise=.4)    \n",
    "\n",
    "colors = ['orange', 'blue'] \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "for i in range(len(X)):\n",
    "    ax.scatter(X[i,0], X[i,1], color=colors[yn[i].int()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data into dataloader\n",
    "X_train = torch.Tensor(X).to(device)\n",
    "y_train = torch.LongTensor(yn.long()).to(device)\n",
    "\n",
    "train = data.TensorDataset(X_train, y_train)\n",
    "trainloader = data.DataLoader(train, batch_size=len(X), shuffle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Learner**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define Learner - we will use MSE Loss\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model(x)\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch      \n",
    "        y_hat = self.model(x)   \n",
    "        loss = nn.CrossEntropyLoss()(y_hat, y)\n",
    "        logs = {'train_loss': loss}\n",
    "        return {'loss': loss, 'log': logs}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.005)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define Hamiltonian and DEFunc\n",
    "HamFunc = HNN(nn.Sequential(\n",
    "            nn.Linear(2,64),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(64,64),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(64,1)    \n",
    ")).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define Neural ODE with Hamiltonian vector field \n",
    "model = nn.Sequential(\n",
    "    NeuralDE(HamFunc,\n",
    "             solver='dopri5',\n",
    "             sensitivity='adjoint'),\n",
    "    nn.Linear(2,2)\n",
    ").to(device)\n",
    "# We append a linear out layer after NeuralDE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type       | Params\n",
      "-------------------------------------\n",
      "0 | model | Sequential | 4 K   \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f16d9e94170f461281dc824070cb2358",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the HNN with adjoint gradient just like any other model in torchdyn\n",
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=200, max_epochs=250)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot Trajectories in the phase space**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_span = torch.linspace(0, 1, 100)\n",
    "traj = model[0].trajectory(X_train, s_span).detach().cpu()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_2D_depth_trajectory(s_span, traj, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAADkCAYAAABqi5P0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAeQUlEQVR4nO2deXhV1dX/Pys3CWEOaAizICIgyKARRHFCQaVVRGurrxNORatvcWi1Dm3pz6I44Fi1YvWh1aLFAaQqDiiDM4MD4AgiyEyYTAIJZNi/P9bJyyXcm9yEO5x77/o8z31yztl7n7Pu8M3a49rinMMwjMSTkWgDDMNQTIyG4RNMjIbhE0yMhuETTIyG4RNMjIbhE0yMYRCRLiLiRCQzAc++QETeiuL95ojIFdG6nxEb0l6MIrJSREpFpCTo1T6RNjnn/u2cG96QsiIyTkSejbZN0X6uiJwoImtiaVOykfZi9DjDOdcs6LUu0QYZaYhzLq1fwErglBDXuwAOyPTO2wMzgK3AcuBK73oOUAoc6J3fBlQALbzzO4AHveMRwFdAMbAW+F0Ym0YD7wedO+AqYBmwHXgUkBDlTgN2A+VACfCFd32OZ8cH3rPfqrbXSz8a+NC79xfAibV8Xjd7thcD3wIn1/LcS4GvvbwrgDHe9abeZ1bl5S/xPt8M4A/A98AWYCrQuhZbRnv3LQZ+AC4Iuv4B8DfgJ+Ab4OSgciHtCkofCXwOFHm2nOZdbwk8Baz3PoO/AoGo/RYTLYZEv+ohxnnAY574+gOFwNCgtHO847e8L/D0oLRR3vF64DjvuBVwRD3E+CqQC3T2nn1amLLjgGdrXJvj2XQo0Ng7n+CldfB++CM8MQzzzvNC3LsHsBpoH/QZdavluT8DugECnADsrH7PwInAmhr5xwIfAx2BRsATwHNh3mdTTyw9vPN2QO+gz68CuB7IAn6FirJ1BHYN9PIO8z6PDkBPL22aZ1NToA0wnxpC3q/fYqLFkOgXKsYS1CtsB6bXFCPQCagEmgeVuwuY7B3fATzs5d3g/agmsMdrHuDl+xEYg+c1a7FpNPuKcUjQ+VTgD2HKhhLFHOD2oPPfAG94xzcDz9TI/yZwSYh7HwJsAk4Bsup6bojy04Gx3nEoMX7N3h6sHeptM0Pcq6n3fZ0DNA7x+a0jqPbgCeeiCOx6AnggRJ58YFfws4DzgdnR+i1am1E5yzmX673OCpHeHtjqnCsOurYK/a8JMBf9cR0BLAHeRv/jHg0sd85t8fKdg3qgVSIyV0QG18PGDUHHO4Fm9ShbW/mDgHNFZHv1CxiCCmEvnHPLgetQ4W0Skedr6+wSkdNF5GMR2erddwRwYC02HgRMC7Lja/SfYL6I/D2og+1W59wO1ONdBawXkddEpGfQvdY6TzEeq9DvsS67OqG1iFC2ZXnPqrbvCdRDRgUTY2SsA1qLSPOga53RdgNoe6sHMAqY65z7yksfgQoVAOfcAufcSPQLnI56uGhT32U4q1HPmBv0auqcmxDy5s5Ncc4NQX+cDrg71HNFpBHwEnAfkO+cywVeR6uG4excjVbvg23Jcc6tdc5d5fZ0sN3p2fKmc24Y+o/jG+DJoHt1EBEJOu8MrIvArtVoFTaUbbvQtna1bS2cc71DfU4NwcQYAc651ajg7hKRHBHpC1wOPOul7wQWAdewR3wfov+15wKISLY3ftjSOVeOtneqYmDuRqCLiET63T4LnCEip4pIwHt/J4pIx5oZRaSHiAz1ftBl7OmECfXcbLTdVwhUiMjpQPBwzUbgABFpGXTt78B4ETnIe16eiIwMZbSI5IvISBFpioqkhL0/zzbAb0UkS0TOBXqhoqvLrqeAS0XkZBHJEJEOItLTObce7Q+YKCItvLRuInJC2E+2npgYI+d8tB25Dm3I/9k5NysofS5ajZkfdN4c7cCp5iJgpYgUoUK9IAZ2vuD93SIin9aV2ftHMxK4Ff2BrgZ+T+jfRiO0LbwZrfa2AW4J9VyvSv9b1PtvA/4H7Y2ufu43wHPACq/a1x54yMvzlogUo505g8KYngHcgH4fW9FmwdVB6Z8A3T1bxwO/cM5ticCu+Whv6wNoR85ctBYAcDEq5q+8si8SojrfUGTvarVhJD8iMhq4wqtOJw3mGQ3DJ5gYDcMnWDXVMHyCeUbD8AkmRsPwCXFfqxcPDjzwQNelS5dEm2EY+7Bo0aLNzrm8UGkpKcYuXbqwcOHCRJthGPsgIqvCpVk11TB8gonRMHyCidEwfIKJ0TB8gonRMKJFVSVU7ISqigYVNzEaxv5SVQGbl8CiW6HwE6jY0aDbpOTQhmHEjR2b4PPbYet8QKDJQZB/fINuZWI0jIby9WRY9jfYsRxcBrQaCHlHQkagQbczMRpGfSneAnPOgOIv0IAHQM5h0PMyaBNuLXTdmBgNoz588wp8eg4aJ6uafGh3KnQ+Z79ubR04hhEps8fCp2extxBbQMfToP8tEGhY9bQa84yGEQnPHQHusxoXm0Hro6HnWGh8wH4/wsRoGLXhHDx3ABp/Kpgm0PJIOPxGyOsflUf5ppoqIk+LyCYRWRp0rbWIvC0iy7y/rRJpo5Fm7NwJz2WwrxAbQaNu0P0SaHsi7BWeteH4RozAZHQDlWD+ALzjnOsOvOOdG0bs2fQjTG8aOi3QGXqOga7nQyA7ao/0jRidc/PQ+JfBjAT+6R3/EwgVet8wosuy2TDroNBpgW5wxO0qxqycqD7WN2IMQ74XyRk0aG5+Io0x0oBFj8GCoWES20LfW6DbhRCIfndL0nTgOOeciIQNZScivwZ+DdC5c+e42WWkEO+MhY0Ph0nsBIMmwMHnR62NWBO/e8aNItIOwPu7KVxG59wk51yBc64gLy9kiBHDCM/0M2oRYkvocRF0GhkzIYL/xTgDuMQ7vgR4JYG2GKnKlAGw89UwiU3g4NFw2A2QHaZDJ0r4ppoqIs+hexweKCJrgD+jm6xMFZHL0f31fpk4C42UZEo79t66MpgAdPoF9L4xKoP6deEbMTrnzg+TdHJcDTHSg/JyeKEF/zfROxQHngw9roPmneJikm/EaBhxo7QUpjWpPU/ucTBgPOQNiI9N+L/NaBjRZdumCIQ4BAbcCXkF8bHJwzyjkT5sXAXvdKk9T7MBMPgpaHVoXEwKxjyjkR78+HndQmzSF/r+KSFCBPOMRjqw7F1YUEc/YOM+UPAAdDgpPjaFwDyjkdosfikCIfaGgfdDx6ExHdSvCxOjkbp8PhmW/qL2PI17Qr9x0C7xI2hWTTVSk08egu+vqz1PZgc4YiJ0Pj2hHrEa84xG6vHR3XULMfsQOOoJ3wgRzDMaqcb74+DHv9SeJ+dwGPwotB3iGyGCidFIJd67FVbfVXueJn1h0GPQ7tj42FQPTIxGajDnZlh3T+15ck9QIR5wWHxsqicmRiP5mf17WH9f7Xnyz4aBj0LztvGxqQGYGI3kpk4hBqDzZVAwEXKax82shmBiNJKX2TfVIcRs6H4TDPgjZEYvilusMDEaycmcm2H9vbVkaAqH3wF9xoIkxwieidFIPt67vY7OmuZwxCPQ42JfDV3UhYnRSC4+uBNWj68lQy4MngxdzkwqIYKJ0Ugm5j8Mq26rJUMenPAcdEj8PNOGYGI0koOFk2D52FoytIWTpkG7o+NmUrQxMRr+Z/Hz8N2Y8OmZneHEV6BNdHaDShQmRsPfLH0dloYLHAhkHQxD/+vbWTX1wcRo+JeVH8Hin4VPzz4UTpkJuQfHz6YYYmI0/MmaZfDhMeHTG/WCYW9Ci/jENI0HJkbDf2xeD/NqCQrV6DAY/jY0bx8/m+JAUohRRFYCxUAlUOGci29ASyN+7NgBb9Uispw+MOwtaN4ufjbFiaQQo8dJzrnNiTbCiCHl5fBKs/DpOX1g2CxonprbdCaTGI1U54VaJnPn9IHh70CzNvGzJ84kxwxacMBbIrLI2xTVSDWm1LIld6PeMPzdlBYiJI9nHOKcWysibYC3ReQb59y84Ay2c3ESM6UtsCt0WqPD4NTZ0Cz1N8BNCs/onFvr/d0ETAMGhshjOxcnI1OOBjaGTsvu4XnE9Pg+fS9GEWkqIs2rj4HhwNLEWmVEhZmjgU9Cp2V2VY+Yop01oUiGamo+ME10OUwmMMU590ZiTTL2m48fgW3/DJ2W0QFOez8lhy9qw/didM6tAPol2g4jiqz8Elb8NkxiWzh1HrRIrQH9SPB9NdVIMUpL4cM+YRJbw2lzoVVqzDWtLyZGI76E3TW4BQybDa0TszeiHzAxGvFjSrg2YDac+Drk9Y2rOX7DxGjEh7euBzaESBA4dhq091+4/XhjYjRiz5ofYPODodP6Pw0HjYivPT7FxGjEnnlhOmQO+TMcNjqupvgZE6MRW6YcHvp6/sVw1J/ja4vPMTEasWP5EkJOlmpyFBz/ZNLFNY01JkYjdswP1TvaGk55DbL8v/dFvDExGrFh2qjQ14e8lDYTv+uLidGIPqWlUDp93+udxkDnE+NuTrJgYjSiz7SmIS62hqMmxt2UZMLEaESX9yaggRlq0Hc85IQSqVGNidGIHiUlsPqWEAkt4dBL4m5OsmFiNKLHjDDbdLcZDtmN42tLEmJiNKLDlJ7h0zr+PH52JDEmRmP/efUc4Nvw6SmyF0asMTEa+8ecG6Ho5drzVIXo0DH2wcRoNJz3b4N199edb8ui2NuSApgYjYYx7yb48c4aF6uHLmrMOV32BPy0HJx5yNrYbzGKyM3RMMRIIt4cDWvuDbqQCRm9ILMNSEeQGsGkyr6Bj8bA2ndg11ao3B1Pa5OGekeHE5GpwadAf+DuqFlk+Jupg6BiftCF5tD5SmjSAko3wK5CKN8M27Oh8oc92bZ+BCsmg9sFub2haQfIyIq39b6mIaEai5xzV1SfiMjjUbTH8CulxfDKsVC1ZM+1nEOh4GFo3VOFWLaZrUVNWb8hh56HLyXw3SOwc3H1DWDTAshqAZU7IOMEaJIHEr5yVlEBK1ZA586QU8tWHKlCQ8T41xrnt0XDEMPHFK+GORcFCTETWg2Cgocg70jY/RNrNzZmxhu9Wbs2m5+KsvjZiKM4pu8xtFh6CZQs1GK7C+GnZeoRs3IhcCTkHBDykWvWwMyZEAjAiBHQtm183moiiViMIjIUuADYLiJLgcXAUufc1lgZZ/iAXdvh+39AcbUQm0LecXDkfdC6NwAz32nJU0/BqlWQnQ2tWsF7HwTYsOkwju76MD3LL4JdK4AyKNsKlaVQsgGabdtHjLt3w7PPwgsvQFERjBoFTcJFd0wx6uMZnwauA7KAvsBZQG/gkBjYtRcichrwEBAA/uGcmxDrZxoeG9+DH2dpdTKrHeQNgwH/D1ocRGUlTJ4MkybBDz+oF2vZEvLzobIStmyBWSWDCXT7E93lLijbCK4Mdm2CHd9A4MS9HvXxxzBhAnzyCezcCXl50LGjCjwdqI8YVznnqhepvRALY0IhIgHgUWAYsAZYICIznHNfxcuGtKViF2xdDDnZ0OhwyB8KPa+BnFaAivCxx2D1ahVf06aQlaXHGzdCZiY0awazvv8V7Xp/T7OSmZDZHLLzoOVhkNUS0PLjxsGrr8L27eodGzWCgw+GQYPSo70IEYhRRP4FfAp8LCI3OOciGOWNKgOB5d6eG4jI88BIwMQYayp2QqNc6HopHDgIWnSDgP5kXn4Z/v53WLlShw+d0w6X0lK9tm2bCmvwYNhQ2Ii5m3/DiEMCyO7N0KovdDyTrTta8Kcb4T//US8aPAzZty/cdBN07ZqQd54QIvGMk9GNZ/KB4SIyFvjCey12zsXaS3YAVgedrwEGxfiZBkAgSyd5N2mvxx5ffgkPPKCiKy9XEQUCUFam7bzKSm3nlZfDt9+qd/zgs3xKq27ikLYr2bmuHfff2oJZs+Cnn/Z9bEEBPPggHHNM/N6qH6hTjM65d4F3q89FJBPohQr0KOJYZa0N27k4BmQ1g8yme0VxKy3Vdt3SpSq+8nKtmlYLUkSPCwu1R7SqSq9lZsLTT+dQVNST0tLQj2vRAq6+Gv70p/TptAmm3kMbzrkKYIn3igdrgU5B5x29azXtmgRMAigoKLB5V9GiRjjFf/wD3nkHiovVA4L+FVHhlZXpGuPKShVqVVVkjxk4UL1tunnDYHy/PyOwAOguIl1REZ4H/E9iTUpPliyBp56C9ev3vl5Zqd6xvFyPKyoiv2fXrvD738MVV+g90hnfi9E5VyEi1wJvokMbTzvnvkywWWlHWRmMHw9ff71vWlaWCjBSEWZnw9Ch8Mc/wtFHQ4YtVwCSQIwAzrnXgdcTbUc689BD8PrrOuwQTEaGirCuBRm5uXDKKXDVVXDCCdqGNPbGPhKjTt5+W8cTi4v3TaurTdinD9x9N5x+ukXzrwsTo1Er334LN98MP/5Yv3Jt2sB998FFF8XGrlTExGiEZe1aHWr47LP6lbvgAnj8cWgeJlicERprOhshKSyEK6+E2bMjL9O6NTz/vE70NiHWH/OMxj6sXw+XX65LmCLlyCN1Wlu3brGzK9Uxz2jsxYoVcOGF9RPieefBnDkmxP3FxGj8H59/rh0u775bd17Q8cJbb4VnntH5p8b+YdVUA1BPeN118N13keXPzYV77tF2pREdTIxpTkWFrku8807tPY2ETp3gySfh1FNja1u6YWJMY4qK4K9/1WGIkpLIyvTqBVOmQP/+sbUtHTExpinLluni3RkzIl9ZccwxOmyRTgt+44l14KQhr72mHTXTp0cmxEAARo6EV14xIcYS84xpRGmpTviujlsTCdnZcOmlMHGixrgxYoeJMU1YtgzuuENj1+zYEVmZ5s1h7Fhd6pQuEdoSiYkxxams1OrlfffBRx9FXq5tWxXvZZfZesN4YWJMYbZt0+rlM8/Ub9VF9+4aEGrEiNjZZuyLiTFF+eEH9Wwvvhh6HWI4Bg3SoY4BA2JnmxEaE2OKUVGh1dF774U33tC4NJGQmame8JFHdKMZI/6YGFMI5zTc/v33h45VE44WLXRy+F136bGRGEyMKUJRkVYvH34Y1q2LvFzbtvC738H//q/1mCYaE2OS4xwsWqRxZmbOjHzYAqBHD434NmqU9Zj6ARNjElNWprNpHn9cAwtHSiCgIRIfeACOOip29hn1w8SYpOzaBdOmaY9pfdqHjRvDWWfp8qeOHWNnn1F/TIxJyM6dugPU3XfDpk2Rl8vL0/WHt9xii4H9iIkxyfjwQx3If/nlyMuIaEiM22/XyG0WQNif+PprEZFxwJVAoXfpVi+6eNpRVKT7XDz0kG7XHSmZmTqQP368RvI2/IuvxejxgHPuvkQbkUiWLdPpaU88sWfnp0ho1gzOOENX8XfpEjPzjCiRDGJMa9au1TbeSy/Vr1y7dvDrX8ONN1oM02QhGUaXrhWRxSLytIi0SrQx8aKiQve4//nP6yfEjAzd3+Lee3XpkwkxeUi4ZxSRWUDbEEm3AY8DdwDO+zsRuCzMfVJi52LndMffyZN1HHDbtsjLNm4Mxx0Hf/mLjiMayYW4uvby8gki0gV41TnXp668BQUFbuHChTG3KdpUVcGXX2onzTPP7Lv9Wm20bg2//KVuwd2uXexsNPYPEVnknCsIlZZwz1gbItLOOVe9T+4oYGki7Yklu3bBvHk6GD9rVuTlMjJ02OLqq3Xvw8aNY2ejEVt8LUbgHhHpj1ZTVwJjEmtObCgr0wnekybB999HXq5RIygo0PHD4cNtfmmy42sxOudSenc/52DzZt25aeLE+s2madVK1x/efjv07Bk7G4344WsxpjI7dmh1dPJkXQRcVhZZuYwMXfx7ySUajj83N6ZmGnHExJgAqqq0x/TBB7WdGGkQ4ZwcOPxwXX949tk2rS3VsK8zzlRVwfz5Ogb48ceRCVFEPeDQoVquX7/Y22nEHxNjnKis1BX4Dz8MU6fCxo3ag1oXgYBuNHP++VotbdMm9rYaicHEGAfKy3U2zYMPwhdf6BKoSAJFNWkCvXvrsMUFF1hYjFTHxBhDKis1JMa//qWdNBs3akdNRUXt5TIzNTDU8cfDzTfbbJp0wcQYI0pLdQfgRx/VHYG3b9cZNXWtusjO1hk0554L118P7dvHx14j8ZgYY8CqVfD227oAePFi3fuwrEzHFcMRCGhvaa9eutrioov03EgfTIxRpLxcFwF/+CE895zGpikqUi8ZTogikJWl1dIhQ9QbDhlis2nSERNjFFm9WrfXfvddWLFCB/ZLS8Pnz8zUV/v2uv/h9ddrz6mRnpgY95Pdu6GwUKulr78On34KW7aoCMMNXYioCBs31till14KF19s+x+mOybG/aCyUocqpk6F997TWTVFRdo+DDd0kZmp7cPcXO0lve467TW1aqlhYmwgq1bpVLZZs9QbFhZqR01paehZNYGAvqqrpWeeCddea9tyG3swMTaAzZvVG772ms6q2b5dt10LNdm7uoNGRAfxe/TQSd4XXmixS429MTHWg927YcECFeG8edph89NP4WfUVIswO1sDCJ90kg5ZWLXUCIWJMULKy3WoYsoUneC9fv2eamnNGTXVAqz2hv366XbcZ5wBLVsmxn7D/5gYI2DNGh3AnzcPvvlGp7UVF4fuLc3OVq+XmQn5+TBsmA5ZHHpo/O02kgsTYy04p23Cl1+G6dN17HD7dvWGNYNFBQIqxEBAvWGfPvCb36g3tAneRiSYGMNQUqKRvKdMgdmzYcMGHbbYuXPf+aWNG6s3zM7WQfvzzoPRoy1Km1E/TIwhcA6WLNEAUR98oLFLQ1VLs7JUiCJaJe3XD264Qfe2EEmM7UbyYmIMwjkNp//SS9pjuny5VktLSvbtLW3cWD1h8+YaKvGaazQURiCQGNuN5MfE6FFSonNK//1v7aQpLFQh1lxtkZWlAmzSRKukQ4bofhb5+Ymz3UgNTIyo8ObOhf/8R5c8bd2q7cPgTppAQL1h69bQt6+OFQ4erGI0jGiQ9mIsL4cXX4QZM7TDZsOGvae0ZWSoN8zN1RCJo0bp7JmOHa1daESXtBZjWZnOLa1ebbF9u/aUOrdnZUXLlrq34THHwK9+BQMHWohEIzb44mclIucC44BewEDn3MKgtFuAy4FK4LfOuTej8cziYpg5U3d6Wrp0T0iMqirtmGnaVNuExx6rAaF69jQRGrHFLz+vpcDZwBPBF0XkMOA8oDfQHpglIoc65+qxf+++rF0LEybAf/+rs2mqvWH1UEWPHrrl9pln6jCF9ZAa8cAXYnTOfQ0g+zbCRgLPO+d2AT+IyHJgIPBRQ59VWAiPPw7TpmlHTWWlerzcXI3WffLJ+howwCZzG/HFF2KshQ7Ax0Hna7xrDWLXLu2sWbZMxVdersuYjjgCxoyBI4/UDWUMIxHETYy17VDsnHslCvevc+fi6nikQ4fq0MS2bVodPfZY84JG4ombGJ1zpzSg2FogOERTR+9aqPtPAiaB7lwcKk8goPFIS0u1gyYQsOEJwz/43R/MAM4TkUYi0hXoDszfnxtmZ+twRWamCdHwF74Qo4iMEpE1wGDgNRF5E8A59yUwFfgKeAO4Zn97Ug3Dr/iiA8c5Nw2YFiZtPDA+vhYZRvzxhWc0DMPEaBi+wcRoGD5BXG1bIyUpIlIIrEq0HRFyILA50UZEgVR4H/F4Dwc55/JCJaSkGJMJEVnonCtItB37Syq8j0S/B6umGoZPMDEahk8wMSaeSYk2IEqkwvtI6HuwNqNh+ATzjIbhE0yMPkBExonIWhH53HuNSLRNkSIip4nItyKyXET+kGh7GoqIrBSRJd7nv7DuEjGwwaqpiUdExgElzrn7Em1LfRCRAPAdMAxd+L0AON8591VCDWsAIrISKHDOJWys1DyjsT8MBJY751Y453YDz6OhUowGYGL0D9eKyGIReVpEkiX4RwdgddD5foVFSTAOeEtEFnlRI+KOiTFOiMgsEVka4jUSeBzoBvQH1gMTE2psejLEOXcEcDpwjYgcH28DfLGeMR2INOyIiDwJvBpjc6JFxGFR/I5zbq33d5OITEOr4PPiaYN5Rh8gIsE7OY5C48gmAwuA7iLSVUSy0Ri3MxJsU70RkaYi0rz6GBhOAr4D84z+4B4R6Y+2W1YCYxJrTmQ45ypE5FrgTSAAPO2FSkk28oFpXtzeTGCKc+6NeBthQxuG4ROsmmoYPsHEaBg+wcRoGD7BxGgYPsHEaBg+wcRoGD7BxGgYPsHEaOyDiJwsIs8k2o50w8RohKIf8FmijUg3TIxGKPoBbUVknoj8KCIN2VvTqCcmRiMU/YBC59zxwFjgggTbkxbYRHFjL0QkCziAPWsqs4Dt3mqGx4DdwBzn3L8TZGLKYp7RqEkv4AvnXJV33hddTnQ28KJz7krgzEQZl8qYGI2a9AO+CDrvCyxGFw5Xh9iw3aNjgInRqEk/VHzV9EE94xpUkGC/m5hg6xmNiPDajH8DyoD3rc0YfUyMhuETrLphGD7BxGgYPsHEaBg+wcRoGD7BxGgYPsHEaBg+wcRoGD7BxGgYPsHEaBg+4f8DoUKwL1AClRUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_2D_state_space(traj, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_2D_space_depth(s_span, traj, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot Learned Hamiltonian Function over vector field**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Learned Hamiltonian & Vector Field')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_grid =  50\n",
    "x = torch.linspace(-3,3,n_grid)\n",
    "Q, P = torch.meshgrid(x,x)\n",
    "H, U, V = torch.zeros(Q.shape), torch.zeros(Q.shape), torch.zeros(Q.shape)\n",
    "for i in range(n_grid):\n",
    "    for j in range(n_grid):\n",
    "        x = torch.cat([Q[i,j].reshape(1,1),P[i,j].reshape(1,1)],1).to(device)\n",
    "        H[i,j] = model[0].defunc.m.H(x).detach().cpu()\n",
    "        O = model[0].defunc(0,x).detach().cpu()\n",
    "        U[i,j], V[i,j] = O[0,0], O[0,1]\n",
    "        \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.contourf(Q,P,H,100,cmap='RdYlBu')\n",
    "ax.streamplot(Q.T.numpy(),P.T.numpy(),U.T.numpy(),V.T.numpy(), color='black')\n",
    "ax.set_xlim([Q.min(),Q.max()])\n",
    "ax.set_ylim([P.min(),P.max()])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"Learned Hamiltonian & Vector Field\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py37",
   "language": "python",
   "name": "py37"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
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   "types_to_exclude": [
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   "window_display": false
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 },
 "nbformat": 4,
 "nbformat_minor": 4
}
